# Nonmonotonic inference operations

@article{Freund1993NonmonotonicIO, title={Nonmonotonic inference operations}, author={Michael Freund and Daniel J. Lehmann}, journal={Log. J. IGPL}, year={1993}, volume={1}, pages={23-68} }

A. Tarski proposed the study of infinitary consequence operations as the central topic of mathematical logic. He considered monotonicity to be a property of all such operations. In this paper, we weaken the monotonicity requirement and consider more general operations, inference operations. These operations describe the nonmonotonic logics both humans and machines seem to be using when infering defeasible information from incomplete knowledge. We single out a number of interesting families of…

## 17 Citations

### Nonmonotonic reasoning: from finitary relations to infinitary inference operations

- MathematicsStud Logica
- 1994

This paper weakens the monotonicity requirement and considers more general operations, inference operations, which describe the nonmonotonic logics both humans and machines seem to be using when infering defeasible information from incomplete knowledge.

### Compactness Properties of Nonmonotonic Inference Operations

- MathematicsJELIA
- 1994

It is proved that minimal reasoning in propositional logic is weakly supracompact and that the associated inference operator is uniquely determined by its finitary restriction via an extension operator Δ4.

### Deductive Nonmonotonic Inference Operations: Antitonic Representations

- MathematicsJ. Log. Comput.
- 1995

The results provide a satisfactory notion of pseudo-compactness, generalizing to deductive nonmonotonic operations the notion of compactness for monotonic ops and provide an alternative, more elegant and more general proof of the existence of an infinitary deductive extension for any finitary deductives operation.

### Generalized Compactness of Nonmonotonic Inference Operations

- Computer ScienceJ. Appl. Non Class. Logics
- 1995

Compactness properties play a fundamental in the study of non-monotonic inference, and in the paper several new versions of compactness are studied.

### ON GENERALIZATIONS OF CONSEQUENCE OPERATION

- Mathematics, Philosophy
- 2007

We define some classes of operation generalizing the notion of logical consequence operation. Then we investigate them in terms of properties of their theories. Kraus Lehmann and Magidor in [2]…

### Nonmonotonic Logics and Semantics

- Computer ScienceJ. Log. Comput.
- 2001

A more general semantics is described in this paper, based on a set of natural properties of choice functions, which is shown to be equivalent to a semantics based on comparing the relative "importance" of sets of models, by what amounts to a qualitative probability measure.

### A Formula-Preferential Base for Paraconsistent and Plausible Reasoning Systems

- Computer Science
- 2001

A general framework for constructing natural consequence relations for paraconsistent and plausible nonmonotonic reasoning is provided, based on preferential systems whose preferences are based on the satisfaction of formulas in models.

### Formula-Preferential Systems for Paraconsistent Non-Monotonic Reasoning (an extended abstract)

- Computer Science
- 2001

A general framework for constructing natural consequence relations for paraconsistent and plausible nonmonotonic reasoning is provided, based on preferential systems whose preferences are based on the satisfaction of formulas in models.

### Defaults as restrictions on classical Hilbert-style proofs

- PhilosophyJ. Log. Lang. Inf.
- 1994

It is proposed to describe default logic as a logic where the juxtaposition of default proofs is subordinate to a restriction condition Ψ, and to prove cumulativity for any default logic (L, Ψ) by slightly modifying the notion of default proof.

### Characterizations of Preferential Entailments

- PhilosophyLog. J. IGPL
- 2002

The paper provides a characterization result for four kinds of preferential entailments of propositional logic, and it appears that the apparently most complicated notion possesses by far the simplest characterization result.

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